Objective: Digital tomosynthesis (DTS) is a type of limited-angle Computed Tomography (CT) used in orthopedic and oncology care to provide a pseudo-3D reconstructed volume of a body part from multiple X-ray projections. Patient motion during acquisitions results in artifacts which affect screening and diagnostic performances. Hence, accurate reconstruction of moving body parts from a tomosynthesis projection series is addressed in this paper, with a particular focus on the breast. The aim of this paper is to assess the feasibility of a novel dynamic reconstruction technique for DTS and evaluate its accuracy compared to an available ground truth. Approach: The proposed method is a combination of a 4D dynamic tomography strategy leveraging the formalism of Projection-based Digital Volume Correlation (P-DVC) with a multiscale approach to estimate and correct patient motion. Iterations of two operations are performed: i) a motion-corrected reconstruction based on the Simultaneous Iterative Reconstruction Technique (SIRT) algorithm and ii) a motion estimation from projection residuals, to obtain motion-free volumes. Performance is evaluated on a synthetic Digital Breast Tomosynthesis (DBT) case. Three slabs of a CIRS breast phantom are imaged on a Senographe Pristina™, under plate-wise rigid body motions with amplitudes ranging up to 10 mm so that an independent measurement of the motion can be accessed. Results: Results show a motion estimation average precision down to 0.183 mm (1.83 voxels), when compared to the independent measurement. Moreover, an 84.2% improvement on the mean residual error and a 59.9% improvement on the root mean square error (RMSE) with the original static reconstruction are obtained. Significance: Visual and quantitative assessments of the dynamically reconstructed volumes show that the proposed method fully restores conspicuity for important clinical features contained in the phantom.